Question

When you push a child on a swing, your action is most effective when your pushes are timed to coincide with the natural frequency of the motion. You are swinging a 30 kg child on a swing suspended from 5 meter cables.Estimate the optimum time interval between your pushes. Would your answer be different if the child had a different mass?

Answer 1

`T = 4.48 s`

we can see that this time period is independent of the mass of the child so answer would be same if the child mass is different

Step-by-step explanation:

Natural frequency of a simple pendulum of L length is given as

`f = (1)/(2\pi)\sqrt{(g)/(L)}`

so the time period of the oscillation is given as

`T = 2\pi \sqrt{(L)/(g)}`

so we will have

`L = 5 m`

`T = 2\pi\sqrt{(5)/(9.81)}`

`T = 4.48 s`

also from above formula we can see that this time period is independent of the mass of the child so answer would be same if the child mass is different